名校
1 . 给出定义:对于函数
,则称向量
为函数
的特征向量,同时称函数
为向量
的特征函数.
(1)设向量
分别为函数
与函数
的特征向量,求
;
(2)设向量
的特征函数为
,且
,
,求
的值;
(3)已知
分别为
三个内角
的对边,
,设函数
的特征向量为
,且
,
分别是边
的中点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/651055fdc939ef20d1e92e82e6b32f36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33309290491d336f5a69dd4308223cc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33309290491d336f5a69dd4308223cc8.png)
(1)设向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c02bd32ab64d9c9cdf154e86e5eb59c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89deb3ed56b145b87f4711a49b8ab094.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc66d7d60e63dced6a4538c60d09b5c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd1e54da5895696a5505e9322cfede9b.png)
(2)设向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1353a012fe272dffbfac0bd9d9bd7b44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d78eab267923d207c5518adb9053b069.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b09e347dae4283fa86f65569a576276.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de7d5ef3a3d9a03be91135fc426d57cc.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82f823fe57e96d1a820acadede21940c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aeae90a042dc659a868a8997f1a0736.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e257e6c38a24ced4f9423f7f51b0e92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/622e4b02aae76d54b295df9890c1d2a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dec2ca6438c82b43f746057d8129885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/295f5a1e09ac16dbedad157b16ca2ba8.png)
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名校
解题方法
2 . 对任意两个非零的平面向量
和
,定义:
;
.若平面向量
满足
,且
和
都在集合
中,则
的值可能为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ce7f5b1bfb32ebc6955eb612b14098f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85a4e782971ff80ad56243d225b906a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e8b95a61af300412fc65f846089028.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b123b0eeb7f0575087577eb3adc50ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5bb7c28c450198e14a6003c8429ea4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9000860e1d6cde8e3f21b47a37dcd9ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50043ddc2b1e8bc0fbddc1fdac797e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9099adf2971b5b87c20f608c38076df5.png)
A.1 | B.![]() | C.![]() | D.![]() |
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2024-04-19更新
|
277次组卷
|
5卷引用:福建省龙岩市连城县第一中学2023-2024学年高一下学期5月月考数学试题
福建省龙岩市连城县第一中学2023-2024学年高一下学期5月月考数学试题内蒙古名校联盟2023-2024学年高一下学期期中联考数学试题(已下线)模块一 专题4 平面向量的数量积 B提升卷(人教B版)(已下线)模块一 专题5 平面向量的数量积 B提升卷(北师大版高一期中)广东省梅州市曾宪梓中学2023-2024学年高一下学期期中联考数学试卷
名校
解题方法
3 . 锐角
中,内角A,B,C所对的边分别为a,b,c,且
,若
,则
面积S的取值范围______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a865a456da9c5d876f6674b790695f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03837b3769eda7f0d3804cc5ad4a6d60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
您最近一年使用:0次
2024-04-09更新
|
1063次组卷
|
4卷引用:福建省漳平第二中学2023-2024学年高一下学期第二次月考数学试题
福建省漳平第二中学2023-2024学年高一下学期第二次月考数学试题河南省周口市西华县第二高级中学2023-2024学年高一下学期第一次月考数学试题(已下线)专题5 解三角形的实际应用问题【讲】(高一期末压轴专项)(已下线)【讲】专题4 解三角形的范围(最值)问题(压轴小题)
解题方法
4 . 已知函数
,若
的值域为
,则实数
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/365578ba776509c73562f25395af625e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3814eb9efb5ccd9969ac39bcfbd0ce05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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5 . 已知
是定义在
上且不恒为零的函数,对于任意实数
,
满足
,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/284042c4d3e634870ccc30d49521dd13.png)
_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b1e393134de4106280668f90d9eac88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3587ff064f9af01371279ab75d22116c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/284042c4d3e634870ccc30d49521dd13.png)
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6 . 已知
在
上是单调函数,对任意
满足
,且
.设函数
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e127d1fbdddd16be623a3a12ee21271.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f57567e757ab2bd2c967cc6a4fbb4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94da61bc50aed56f8118e4bf965e1265.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c404bec03f3ac7aea396a0960d5409d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54094ef9c659507396c6051ce77f4c2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17aa6bee964fc23b7a86adc2f559aa3f.png)
A.函数![]() |
B.若函数![]() ![]() ![]() |
C.函数![]() |
D.函数![]() ![]() |
您最近一年使用:0次
7 . 已知函数
,
.
(1)若函数
在
为增函数,求实数
的取值范围;
(2)当
时,
,函数
在区间
上的值域为
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da77594b6176f65b59863e02c144852e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c80cb910ebdc2457ef24e2b07b59af1a.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe86cace140f2c3588ab115837bbfc9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a882037b9ce104ecc496e0f31a139361.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a1c75ed22b86d7fae5b7ca9f34eb9b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9829ad49f32fb73dbde8d1d18ab3308e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/351629c193354cdcf202133052e45028.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a676bd44a087927c5878d0e8e9cdba13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
8 . 已知函数
,
.
(1)若函数
,
,求
的最值;
(2)设函数
,
在区间
上连续不断,证明:函数
有且只有一个零点
,且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7edecfbf1b4e1052468d209e8f017a88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dce2bfe6e1fde9265d2a07c42bbdf58.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31bfb22bf37b71482bd4649852a7dacc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0eac2b31a19918895e5af2d316490e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cc17049fc86f1ef6b73f8a14fc24d41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f77f8111c7805e673a644b0a690dcc.png)
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9 . 已知函数
的图象关于直线
对称,其最小正周期与函数
相同.
(1)求
的单调递减区间;
(2)设函数
,证明:
有且只有一个零点
,且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37c676060db70571815dd981284bbdde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70c6cb0cc172657611e286e7fa669584.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4eaf01c25190326228208b2bb7cb096.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/162c3e8cf21a53417be8e959c4bd7897.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1299ce9bf7d2ddda2d792a1d8381db35.png)
您最近一年使用:0次
10 . 已知定义在
上的函数
满足
,当
时,
,且
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a28068770a85b88b42321cd71ecd3c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32e6418f7cf018c9a78b40642c95e445.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e541ea2f855f981c96207070683d388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b666663ce3537a634a3b427b418eb62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d87cd4403487962c38c8707ba3ab3fa3.png)
A.![]() | B.![]() |
C.![]() | D.![]() ![]() |
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